Related papers: Forced patterns near a Turing-Hopf bifurcation
A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation…
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by…
We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced…
The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We investigate the relationship between the linear surface wave instabilities of a shallow viscous fluid layer and the shape of the periodic, parametric-forcing function (describing the vertical acceleration of the fluid container) that…
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
The question of the termination of a periodic spatial structure of Turing type in a growing system is addressed in a chemical engineering perspective and a biomimetic approach. The effects of the dynamical parameters on the stability and…
The effects of external forcing on a turbulent, liquid-fuelled, swirl-stabilized gas turbine combustor operating at a pressure of approximately 1 MPa are explored experimentally. In particular, the dynamics and coupling between the…
We furnish necessary and sufficient conditions for the occurrence of a Hopf bifurcation in a particularly significant fluid-structure problem, where a Navier-Stokes liquid interacts with a rigid body that is subject to an undamped elastic…
A method of random forcing with a constant power input for two-dimensional gyrokinetic turbulence simulations is developed for the study of stationary plasma turbulence. The property that the forcing term injects the energy at a constant…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
The study of collective excitations is a crucial tool for understanding many-body quantum systems. For instance, they play a central role in the exploration of superfluidity and other quantum macroscopic phenomena in Bose and Fermi systems.…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
We study the spatial fluctuations of transient creep deformation of materials as a function of time, both by Digital Image Correlation (DIC) measurements of paper samples and by numerical simulations of a crystal plasticity or discrete…
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the…